Competition between direct process and stepwise process in multiphoton stripping of atoms. A model calculation in helium

We analyse the processes responsible for the formation of doubly charged ions by multiphoton absorption. A++ ions can be created through two different processes, either by a direct multiphoton absorption from A atoms (A → A++) or by a stepwise process via A + ions (A → A+, A+ → A++). By using a simple theoretical model we discuss the distinction between the two mecanisms : direct process corresponds to a yield of A++ ions proportional to the interaction time while stepwise process corresponds to a yield proportional to the square of the interaction time. We obtain a mathematical definition of the direct process and propose a method to calculate its probability. Quantitative results are presented for the case of the ionization of helium ground state, when double ionization by direct process requires two photons, while stepwise process involves two or three photons. These results can be generalized to more complicated processes. Direct process is expected to be negligible unless the number of photons it requires is smaller than the number of photons involved in stepwise process.